# Linear expansion distance problem

On a hot day where the temperature is 32 degrees celsius, the distance between two lamp posts on the road is 30m as measured by a metal tape whose coefficient of linear expansion is hypothetically 50 x 10^-6 /degree Celsius. If the tape gives its correct reading at 20 degrees celcius, what is the actual distance between the lamp posts?

## Answers and Replies

LowlyPion
Homework Helper
How would you think to go about solving the problem?

Any equations come to mind?

i derived the formula alpha = change in L / (original length x change in temperature)
i came up with a formula original length = final length / (alpha x change in temperature + 1)
alpha is the coefficient of linear expansion..
I set the original length as the original length of the tape and not the actual distance between the 2 posts..
I got 29.98m
i subtracted it to 30m and i got 0.018m..
i added it to 30m to get the actual distance of the 2 posts..

My answer is 30.018m..

Is that right?

LowlyPion
Homework Helper
i derived the formula alpha = change in L / (original length x change in temperature)
i came up with a formula original length = final length / (alpha x change in temperature + 1)
alpha is the coefficient of linear expansion..
I set the original length as the original length of the tape and not the actual distance between the 2 posts..
I got 29.98m
i subtracted it to 30m and i got 0.018m..
i added it to 30m to get the actual distance of the 2 posts..

My answer is 30.018m..

Is that right?

Looks right. If the tape was cooled by 12 degrees it would contract by .018 m. Hence it will read higher than the measure at the warmer temperature by that amount.